On a class of algorithms for total approximation
Let A be a given \(m\times n\) matrix and let \(b\in {\mathbb{R}}^ n\) with \(m>n\) and define \(Z:=(A,b)\). The following total approximation problem is considered: Find \(v\in {\mathbb{R}}^{n+1}\) to minimize \(\| Zv\|_ p\) such that \(\| v'\|_ q=1\) where \(p+q=pq\) and v' is obtained from v by deleting the first k components (usually \(k=0)\). A class of algorithms is proposed and a local convergence analysis as well as a partial global convergence analysis for it are given.
scientific article; zbMATH DE number 3932276